簡約 (2m^3n^4p^2)^3

解

簡約

(2 m^{3} n^{4} p^{2})^{3}

8 m^{9} n^{12} p^{6}

解答ステップ

(2 m^{3} n^{4} p^{2})^{3}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

(2 m^{3} n^{4} p^{2})^{3} = 2^{3} (m^{3})^{3} (n^{4})^{3} (p^{2})^{3}

= 2^{3} (m^{3})^{3} (n^{4})^{3} (p^{2})^{3}

2^{3} = 8

= 8 (m^{3})^{3} (n^{4})^{3} (p^{2})^{3}

簡素化

(m^{3})^{3} : m^{9}

= 8 m^{9} (n^{4})^{3} (p^{2})^{3}

簡素化

(n^{4})^{3} : n^{12}

= 8 m^{9} n^{12} (p^{2})^{3}

簡素化

(p^{2})^{3} : p^{6}

= 8 m^{9} n^{12} p^{6}